// SPDX-License-Identifier: Apache-2.0

package chisel3.util.random

import chisel3._

/** A reduction operation for an LFSR.
  * @see [[XOR]]
  * @see [[XNOR]]
  */
sealed trait LFSRReduce extends ((Bool, Bool) => Bool)

/** XOR (exclusive or) reduction operation */
object XOR extends LFSRReduce {
  def apply(a: Bool, b: Bool): Bool = a ^ b
}

/** Not XOR (exclusive or) reduction operation */
object XNOR extends LFSRReduce {
  def apply(a: Bool, b: Bool): Bool = !(a ^ b)
}

/** Trait that defines a Linear Feedback Shift Register (LFSR).
  *
  * $seedExplanation
  * @see [[FibonacciLFSR]]
  * @see [[GaloisLFSR]]
  * @see [[https://en.wikipedia.org/wiki/Linear-feedback_shift_register]]
  *
  * @define paramWidth @param width the width of the LFSR
  * @define paramTaps @param taps a set of tap points to use when constructing the LFSR
  * @define paramSeed @param seed an initial value for internal LFSR state. If [[scala.None None]], then the LFSR
  * state LSB will be set to a known safe value on reset (to prevent lock up).
  * @define paramReduction @param reduction the reduction operation (either [[chisel3.util.random.XOR XOR]] or
  * [[chisel3.util.random.XNOR XNOR]])
  * @define paramStep @param step the number of state updates per cycle
  * @define paramUpdateSeed @param updateSeed if true, when loading the seed the state will be updated as if the seed
  * were the current state, if false, the state will be set to the seed
  * @define seedExplanation If the user specifies a seed, then a compile-time check is added that they are not
  * initializing the LFSR to a state which will cause it to lock up. If the user does not set a seed, then the least
  * significant bit of the state will be set or reset based on the choice of reduction operator.
  */
trait LFSR extends PRNG {

  /** The binary reduction operation used by this LFSR, either [[chisel3.util.random.XOR XOR]] or
    * [[chisel3.util.random.XNOR XNOR]]. This has the effect of mandating what seed is invalid.
    */
  def reduction: LFSRReduce

  override protected def resetValue: Vec[Bool] = seed match {
    case Some(s) =>
      reduction match {
        case XOR  => require(s != 0, "Seed cannot be zero")
        case XNOR => require(s != BigInt(2).pow(width) - 1, "Seed cannot be all ones (max value)")
      }
      super.resetValue

    case None => {
      val res = WireDefault(Vec(width, Bool()), DontCare)

      reduction match {
        case XOR  => res(0) := true.B
        case XNOR => res(0) := false.B
      }

      res
    }
  }
}

/** Utilities related to psuedorandom number generation using Linear Feedback Shift Registers (LFSRs).
  *
  * For example, to generate a pseudorandom 16-bit [[UInt]] that changes every cycle, you can use:
  * {{{
  * val pseudoRandomNumber = LFSR(16)
  * }}}
  */
object LFSR {

  /** Return a pseudorandom [[UInt]] generated using a [[FibonacciLFSR]]. If you require a Galois LFSR, use
    * [[GaloisLFSR$.maxPeriod GaloisLFSR.maxPeriod]].
    * @param width the width of the LFSR
    * @param increment when asserted, the LFSR will increment
    * @param seed an initial seed (this cannot be zero)
    * @return a [[UInt]] that is the output of a maximal period LFSR of the requested width
    */
  def apply(width: Int, increment: Bool = true.B, seed: Option[BigInt] = Some(1)): UInt =
    FibonacciLFSR.maxPeriod(width, increment, seed, XOR)

  /** Utility used to report an unknown tap width */
  private[random] def badWidth(width: Int): Nothing = throw new IllegalArgumentException(
    s"No max period LFSR taps stored for requested width '$width'"
  )

  /** A mapping of widths to a sequence of known LFSR taps that produce a maximal period LFSR. These work for either a
    * [[chisel3.util.random.FibonacciLFSR Fibonacci LFSR]] or a [[chisel3.util.random.GaloisLFSR Galois LFSR]]. Taps are
    * available for bit widths of 2--786, 1024, 2048, and 4096.
    *
    * Users can automatically generate [[LFSR]]s using these taps with [[LFSR.apply]] for a maximum period Fibonacci XOR
    * LFSR or with [[MaxPeriodGaloisLFSR]]/[[GaloisLFSR.maxPeriod]] or
    * [[MaxPeriodFibonacciLFSR]]/[[FibonacciLFSR.maxPeriod]] for more configuration options.
    * @see [[http://courses.cse.tamu.edu/walker/csce680/lfsr_table.pdf]]
    * @see [[https://www.xilinx.com/support/documentation/application_notes/xapp052.pdf]]
    */
  lazy val tapsMaxPeriod: Map[Int, Seq[Set[Int]]] = tapsFirst ++ tapsSecond

  /** First portion of known taps (a combined map hits the 64KB JVM method limit) */
  private def tapsFirst = Map(
    2 -> Seq(Set(2, 1)),
    3 -> Seq(Set(3, 2)),
    4 -> Seq(Set(4, 3)),
    5 -> Seq(Set(5, 3), Set(5, 4, 3, 2)),
    6 -> Seq(Set(6, 5), Set(6, 5, 3, 2)),
    7 -> Seq(Set(7, 6), Set(7, 6, 5, 4)),
    8 -> Seq(Set(8, 6, 5, 4)),
    9 -> Seq(Set(9, 5), Set(9, 8, 6, 5)),
    10 -> Seq(Set(10, 7), Set(10, 9, 7, 6)),
    11 -> Seq(Set(11, 9), Set(11, 10, 9, 7)),
    12 -> Seq(Set(12, 11, 8, 6)),
    13 -> Seq(Set(13, 12, 10, 9)),
    14 -> Seq(Set(14, 13, 11, 9)),
    15 -> Seq(Set(15, 14), Set(15, 14, 13, 11)),
    16 -> Seq(Set(16, 14, 13, 11)),
    17 -> Seq(Set(17, 14), Set(17, 16, 15, 14)),
    18 -> Seq(Set(18, 11), Set(18, 17, 16, 13)),
    19 -> Seq(Set(19, 18, 17, 14)),
    20 -> Seq(Set(20, 17), Set(20, 19, 16, 14)),
    21 -> Seq(Set(21, 19), Set(21, 20, 19, 16)),
    22 -> Seq(Set(22, 21), Set(22, 19, 18, 17)),
    23 -> Seq(Set(23, 18), Set(23, 22, 20, 18)),
    24 -> Seq(Set(24, 23, 21, 20)),
    25 -> Seq(Set(25, 22), Set(25, 24, 23, 22)),
    26 -> Seq(Set(26, 25, 24, 20)),
    27 -> Seq(Set(27, 26, 25, 22)),
    28 -> Seq(Set(28, 25), Set(28, 27, 24, 22)),
    29 -> Seq(Set(29, 27), Set(29, 28, 27, 25)),
    30 -> Seq(Set(30, 29, 26, 24)),
    31 -> Seq(Set(31, 28), Set(31, 30, 29, 28)),
    32 -> Seq(Set(32, 30, 26, 25)),
    33 -> Seq(Set(33, 20), Set(33, 32, 29, 27)),
    34 -> Seq(Set(34, 31, 30, 26)),
    35 -> Seq(Set(35, 33), Set(35, 34, 28, 27)),
    36 -> Seq(Set(36, 25), Set(36, 35, 29, 28)),
    37 -> Seq(Set(37, 36, 33, 31)),
    38 -> Seq(Set(38, 37, 33, 32)),
    39 -> Seq(Set(39, 35), Set(39, 38, 35, 32)),
    40 -> Seq(Set(40, 37, 36, 35)),
    41 -> Seq(Set(41, 38), Set(41, 40, 39, 38)),
    42 -> Seq(Set(42, 40, 37, 35)),
    43 -> Seq(Set(43, 42, 38, 37)),
    44 -> Seq(Set(44, 42, 39, 38)),
    45 -> Seq(Set(45, 44, 42, 41)),
    46 -> Seq(Set(46, 40, 39, 38)),
    47 -> Seq(Set(47, 42), Set(47, 46, 43, 42)),
    48 -> Seq(Set(48, 44, 41, 39)),
    49 -> Seq(Set(49, 40), Set(49, 45, 44, 43)),
    50 -> Seq(Set(50, 48, 47, 46)),
    51 -> Seq(Set(51, 50, 48, 45)),
    52 -> Seq(Set(52, 49), Set(52, 51, 49, 46)),
    53 -> Seq(Set(53, 52, 51, 47)),
    54 -> Seq(Set(54, 51, 48, 46)),
    55 -> Seq(Set(55, 31), Set(55, 54, 53, 49)),
    56 -> Seq(Set(56, 54, 52, 49)),
    57 -> Seq(Set(57, 50), Set(57, 55, 54, 52)),
    58 -> Seq(Set(58, 39), Set(58, 57, 53, 52)),
    59 -> Seq(Set(59, 57, 55, 52)),
    60 -> Seq(Set(60, 59), Set(60, 58, 56, 55)),
    61 -> Seq(Set(61, 60, 59, 56)),
    62 -> Seq(Set(62, 59, 57, 56)),
    63 -> Seq(Set(63, 62), Set(63, 62, 59, 58)),
    64 -> Seq(Set(64, 63, 61, 60)),
    65 -> Seq(Set(65, 47), Set(65, 64, 62, 61)),
    66 -> Seq(Set(66, 60, 58, 57)),
    67 -> Seq(Set(67, 66, 65, 62)),
    68 -> Seq(Set(68, 59), Set(68, 67, 63, 61)),
    69 -> Seq(Set(69, 67, 64, 63)),
    70 -> Seq(Set(70, 69, 67, 65)),
    71 -> Seq(Set(71, 65), Set(71, 70, 68, 66)),
    72 -> Seq(Set(72, 69, 63, 62)),
    73 -> Seq(Set(73, 48), Set(73, 71, 70, 69)),
    74 -> Seq(Set(74, 71, 70, 67)),
    75 -> Seq(Set(75, 74, 72, 69)),
    76 -> Seq(Set(76, 74, 72, 71)),
    77 -> Seq(Set(77, 75, 72, 71)),
    78 -> Seq(Set(78, 77, 76, 71)),
    79 -> Seq(Set(79, 70), Set(79, 77, 76, 75)),
    80 -> Seq(Set(80, 78, 76, 71)),
    81 -> Seq(Set(81, 77), Set(81, 79, 78, 75)),
    82 -> Seq(Set(82, 78, 76, 73)),
    83 -> Seq(Set(83, 81, 79, 76)),
    84 -> Seq(Set(84, 71), Set(84, 83, 77, 75)),
    85 -> Seq(Set(85, 84, 83, 77)),
    86 -> Seq(Set(86, 84, 81, 80)),
    87 -> Seq(Set(87, 74), Set(87, 86, 82, 80)),
    88 -> Seq(Set(88, 80, 79, 77)),
    89 -> Seq(Set(89, 51), Set(89, 86, 84, 83)),
    90 -> Seq(Set(90, 88, 87, 85)),
    91 -> Seq(Set(91, 90, 86, 83)),
    92 -> Seq(Set(92, 90, 87, 86)),
    93 -> Seq(Set(93, 91), Set(93, 91, 90, 87)),
    94 -> Seq(Set(94, 73), Set(94, 93, 89, 88)),
    95 -> Seq(Set(95, 84), Set(95, 94, 90, 88)),
    96 -> Seq(Set(96, 90, 87, 86)),
    97 -> Seq(Set(97, 91), Set(97, 95, 93, 91)),
    98 -> Seq(Set(98, 87), Set(98, 97, 91, 90)),
    99 -> Seq(Set(99, 95, 94, 92)),
    100 -> Seq(Set(100, 63), Set(100, 98, 93, 92)),
    101 -> Seq(Set(101, 100, 95, 94)),
    102 -> Seq(Set(102, 99, 97, 96)),
    103 -> Seq(Set(103, 94), Set(103, 102, 99, 94)),
    104 -> Seq(Set(104, 103, 94, 93)),
    105 -> Seq(Set(105, 89), Set(105, 104, 99, 98)),
    106 -> Seq(Set(106, 91), Set(106, 105, 101, 100)),
    107 -> Seq(Set(107, 105, 99, 98)),
    108 -> Seq(Set(108, 77), Set(108, 103, 97, 96)),
    109 -> Seq(Set(109, 107, 105, 104)),
    110 -> Seq(Set(110, 109, 106, 104)),
    111 -> Seq(Set(111, 101), Set(111, 109, 107, 104)),
    112 -> Seq(Set(112, 108, 106, 101)),
    113 -> Seq(Set(113, 104), Set(113, 111, 110, 108)),
    114 -> Seq(Set(114, 113, 112, 103)),
    115 -> Seq(Set(115, 110, 108, 107)),
    116 -> Seq(Set(116, 114, 111, 110)),
    117 -> Seq(Set(117, 116, 115, 112)),
    118 -> Seq(Set(118, 85), Set(118, 116, 113, 112)),
    119 -> Seq(Set(119, 111), Set(119, 116, 111, 110)),
    120 -> Seq(Set(120, 118, 114, 111)),
    121 -> Seq(Set(121, 103), Set(121, 120, 116, 113)),
    122 -> Seq(Set(122, 121, 120, 116)),
    123 -> Seq(Set(123, 121), Set(123, 122, 119, 115)),
    124 -> Seq(Set(124, 87), Set(124, 119, 118, 117)),
    125 -> Seq(Set(125, 120, 119, 118)),
    126 -> Seq(Set(126, 124, 122, 119)),
    127 -> Seq(Set(127, 126), Set(127, 126, 124, 120)),
    128 -> Seq(Set(128, 127, 126, 121)),
    129 -> Seq(Set(129, 124), Set(129, 128, 125, 124)),
    130 -> Seq(Set(130, 127), Set(130, 129, 128, 125)),
    131 -> Seq(Set(131, 129, 128, 123)),
    132 -> Seq(Set(132, 103), Set(132, 130, 127, 123)),
    133 -> Seq(Set(133, 131, 125, 124)),
    134 -> Seq(Set(134, 77), Set(134, 133, 129, 127)),
    135 -> Seq(Set(135, 124), Set(135, 132, 131, 129)),
    136 -> Seq(Set(136, 134, 133, 128)),
    137 -> Seq(Set(137, 116), Set(137, 136, 133, 126)),
    138 -> Seq(Set(138, 137, 131, 130)),
    139 -> Seq(Set(139, 136, 134, 131)),
    140 -> Seq(Set(140, 111), Set(140, 139, 136, 132)),
    141 -> Seq(Set(141, 140, 135, 128)),
    142 -> Seq(Set(142, 121), Set(142, 141, 139, 132)),
    143 -> Seq(Set(143, 141, 140, 138)),
    144 -> Seq(Set(144, 142, 140, 137)),
    145 -> Seq(Set(145, 93), Set(145, 144, 140, 139)),
    146 -> Seq(Set(146, 144, 143, 141)),
    147 -> Seq(Set(147, 145, 143, 136)),
    148 -> Seq(Set(148, 121), Set(148, 145, 143, 141)),
    149 -> Seq(Set(149, 142, 140, 139)),
    150 -> Seq(Set(150, 97), Set(150, 148, 147, 142)),
    151 -> Seq(Set(151, 148), Set(151, 150, 149, 148)),
    152 -> Seq(Set(152, 150, 149, 146)),
    153 -> Seq(Set(153, 152), Set(153, 149, 148, 145)),
    154 -> Seq(Set(154, 153, 149, 145)),
    155 -> Seq(Set(155, 151, 150, 148)),
    156 -> Seq(Set(156, 153, 151, 147)),
    157 -> Seq(Set(157, 155, 152, 151)),
    158 -> Seq(Set(158, 153, 152, 150)),
    159 -> Seq(Set(159, 128), Set(159, 156, 153, 148)),
    160 -> Seq(Set(160, 158, 157, 155)),
    161 -> Seq(Set(161, 143), Set(161, 159, 158, 155)),
    162 -> Seq(Set(162, 158, 155, 154)),
    163 -> Seq(Set(163, 160, 157, 156)),
    164 -> Seq(Set(164, 159, 158, 152)),
    165 -> Seq(Set(165, 162, 157, 156)),
    166 -> Seq(Set(166, 164, 163, 156)),
    167 -> Seq(Set(167, 161), Set(167, 165, 163, 161)),
    168 -> Seq(Set(168, 162, 159, 152)),
    169 -> Seq(Set(169, 135), Set(169, 164, 163, 161)),
    170 -> Seq(Set(170, 147), Set(170, 169, 166, 161)),
    171 -> Seq(Set(171, 169, 166, 165)),
    172 -> Seq(Set(172, 165), Set(172, 169, 165, 161)),
    173 -> Seq(Set(173, 171, 168, 165)),
    174 -> Seq(Set(174, 161), Set(174, 169, 166, 165)),
    175 -> Seq(Set(175, 169), Set(175, 173, 171, 169)),
    176 -> Seq(Set(176, 167, 165, 164)),
    177 -> Seq(Set(177, 169), Set(177, 175, 174, 172)),
    178 -> Seq(Set(178, 91), Set(178, 176, 171, 170)),
    179 -> Seq(Set(179, 178, 177, 175)),
    180 -> Seq(Set(180, 173, 170, 168)),
    181 -> Seq(Set(181, 180, 175, 174)),
    182 -> Seq(Set(182, 181, 176, 174)),
    183 -> Seq(Set(183, 127), Set(183, 179, 176, 175)),
    184 -> Seq(Set(184, 177, 176, 175)),
    185 -> Seq(Set(185, 161), Set(185, 184, 182, 177)),
    186 -> Seq(Set(186, 180, 178, 177)),
    187 -> Seq(Set(187, 182, 181, 180)),
    188 -> Seq(Set(188, 186, 183, 182)),
    189 -> Seq(Set(189, 187, 184, 183)),
    190 -> Seq(Set(190, 188, 184, 177)),
    191 -> Seq(Set(191, 182), Set(191, 187, 185, 184)),
    192 -> Seq(Set(192, 190, 178, 177)),
    193 -> Seq(Set(193, 178), Set(193, 189, 186, 184)),
    194 -> Seq(Set(194, 107), Set(194, 192, 191, 190)),
    195 -> Seq(Set(195, 193, 192, 187)),
    196 -> Seq(Set(196, 194, 187, 185)),
    197 -> Seq(Set(197, 195, 193, 188)),
    198 -> Seq(Set(198, 133), Set(198, 193, 190, 183)),
    199 -> Seq(Set(199, 165), Set(199, 198, 195, 190)),
    200 -> Seq(Set(200, 198, 197, 195)),
    201 -> Seq(Set(201, 187), Set(201, 199, 198, 195)),
    202 -> Seq(Set(202, 147), Set(202, 198, 196, 195)),
    203 -> Seq(Set(203, 202, 196, 195)),
    204 -> Seq(Set(204, 201, 200, 194)),
    205 -> Seq(Set(205, 203, 200, 196)),
    206 -> Seq(Set(206, 201, 197, 196)),
    207 -> Seq(Set(207, 164), Set(207, 206, 201, 198)),
    208 -> Seq(Set(208, 207, 205, 199)),
    209 -> Seq(Set(209, 203), Set(209, 207, 206, 204)),
    210 -> Seq(Set(210, 207, 206, 198)),
    211 -> Seq(Set(211, 203, 201, 200)),
    212 -> Seq(Set(212, 107), Set(212, 209, 208, 205)),
    213 -> Seq(Set(213, 211, 208, 207)),
    214 -> Seq(Set(214, 213, 211, 209)),
    215 -> Seq(Set(215, 192), Set(215, 212, 210, 209)),
    216 -> Seq(Set(216, 215, 213, 209)),
    217 -> Seq(Set(217, 172), Set(217, 213, 212, 211)),
    218 -> Seq(Set(218, 207), Set(218, 217, 211, 210)),
    219 -> Seq(Set(219, 218, 215, 211)),
    220 -> Seq(Set(220, 211, 210, 208)),
    221 -> Seq(Set(221, 219, 215, 213)),
    222 -> Seq(Set(222, 220, 217, 214)),
    223 -> Seq(Set(223, 190), Set(223, 221, 219, 218)),
    224 -> Seq(Set(224, 222, 217, 212)),
    225 -> Seq(Set(225, 193), Set(225, 224, 220, 215)),
    226 -> Seq(Set(226, 223, 219, 216)),
    227 -> Seq(Set(227, 223, 218, 217)),
    228 -> Seq(Set(228, 226, 217, 216)),
    229 -> Seq(Set(229, 228, 225, 219)),
    230 -> Seq(Set(230, 224, 223, 222)),
    231 -> Seq(Set(231, 205), Set(231, 229, 227, 224)),
    232 -> Seq(Set(232, 228, 223, 221)),
    233 -> Seq(Set(233, 159), Set(233, 232, 229, 224)),
    234 -> Seq(Set(234, 203), Set(234, 232, 225, 223)),
    235 -> Seq(Set(235, 234, 229, 226)),
    236 -> Seq(Set(236, 231), Set(236, 229, 228, 226)),
    237 -> Seq(Set(237, 236, 233, 230)),
    238 -> Seq(Set(238, 237, 236, 233)),
    239 -> Seq(Set(239, 203), Set(239, 238, 232, 227)),
    240 -> Seq(Set(240, 237, 235, 232)),
    241 -> Seq(Set(241, 171), Set(241, 237, 233, 232)),
    242 -> Seq(Set(242, 241, 236, 231)),
    243 -> Seq(Set(243, 242, 238, 235)),
    244 -> Seq(Set(244, 243, 240, 235)),
    245 -> Seq(Set(245, 244, 241, 239)),
    246 -> Seq(Set(246, 245, 244, 235)),
    247 -> Seq(Set(247, 165), Set(247, 245, 243, 238)),
    248 -> Seq(Set(248, 238, 234, 233)),
    249 -> Seq(Set(249, 163), Set(249, 248, 245, 242)),
    250 -> Seq(Set(250, 147), Set(250, 247, 245, 240)),
    251 -> Seq(Set(251, 249, 247, 244)),
    252 -> Seq(Set(252, 185), Set(252, 251, 247, 241)),
    253 -> Seq(Set(253, 252, 247, 246)),
    254 -> Seq(Set(254, 253, 252, 247)),
    255 -> Seq(Set(255, 203), Set(255, 253, 252, 250)),
    256 -> Seq(Set(256, 254, 251, 246)),
    257 -> Seq(Set(257, 245), Set(257, 255, 251, 250)),
    258 -> Seq(Set(258, 175), Set(258, 254, 252, 249)),
    259 -> Seq(Set(259, 257, 253, 249)),
    260 -> Seq(Set(260, 253, 252, 250)),
    261 -> Seq(Set(261, 257, 255, 254)),
    262 -> Seq(Set(262, 258, 254, 253)),
    263 -> Seq(Set(263, 170), Set(263, 261, 258, 252)),
    264 -> Seq(Set(264, 263, 255, 254)),
    265 -> Seq(Set(265, 223), Set(265, 263, 262, 260)),
    266 -> Seq(Set(266, 219), Set(266, 265, 260, 259)),
    267 -> Seq(Set(267, 264, 261, 259)),
    268 -> Seq(Set(268, 243), Set(268, 267, 264, 258)),
    269 -> Seq(Set(269, 268, 263, 262)),
    270 -> Seq(Set(270, 217), Set(270, 267, 263, 260)),
    271 -> Seq(Set(271, 213), Set(271, 265, 264, 260)),
    272 -> Seq(Set(272, 270, 266, 263)),
    273 -> Seq(Set(273, 250), Set(273, 272, 271, 266)),
    274 -> Seq(Set(274, 207), Set(274, 272, 267, 265)),
    275 -> Seq(Set(275, 266, 265, 264)),
    276 -> Seq(Set(276, 275, 273, 270)),
    277 -> Seq(Set(277, 274, 271, 265)),
    278 -> Seq(Set(278, 273), Set(278, 277, 274, 273)),
    279 -> Seq(Set(279, 274), Set(279, 278, 275, 274)),
    280 -> Seq(Set(280, 278, 275, 271)),
    281 -> Seq(Set(281, 188), Set(281, 280, 277, 272)),
    282 -> Seq(Set(282, 247), Set(282, 278, 277, 272)),
    283 -> Seq(Set(283, 278, 276, 271)),
    284 -> Seq(Set(284, 165), Set(284, 279, 278, 276)),
    285 -> Seq(Set(285, 280, 278, 275)),
    286 -> Seq(Set(286, 217), Set(286, 285, 276, 271)),
    287 -> Seq(Set(287, 216), Set(287, 285, 282, 281)),
    288 -> Seq(Set(288, 287, 278, 277)),
    289 -> Seq(Set(289, 268), Set(289, 286, 285, 277)),
    290 -> Seq(Set(290, 288, 287, 285)),
    291 -> Seq(Set(291, 286, 280, 279)),
    292 -> Seq(Set(292, 195), Set(292, 291, 289, 285)),
    293 -> Seq(Set(293, 292, 287, 282)),
    294 -> Seq(Set(294, 233), Set(294, 292, 291, 285)),
    295 -> Seq(Set(295, 247), Set(295, 293, 291, 290)),
    296 -> Seq(Set(296, 292, 287, 285)),
    297 -> Seq(Set(297, 292), Set(297, 296, 293, 292)),
    298 -> Seq(Set(298, 294, 290, 287)),
    299 -> Seq(Set(299, 295, 293, 288)),
    300 -> Seq(Set(300, 293), Set(300, 290, 288, 287)),
    301 -> Seq(Set(301, 299, 296, 292)),
    302 -> Seq(Set(302, 261), Set(302, 297, 293, 290)),
    303 -> Seq(Set(303, 297, 291, 290)),
    304 -> Seq(Set(304, 303, 302, 293)),
    305 -> Seq(Set(305, 203), Set(305, 303, 299, 298)),
    306 -> Seq(Set(306, 305, 303, 299)),
    307 -> Seq(Set(307, 305, 303, 299)),
    308 -> Seq(Set(308, 306, 299, 293)),
    309 -> Seq(Set(309, 307, 302, 299)),
    310 -> Seq(Set(310, 309, 305, 302)),
    311 -> Seq(Set(311, 308, 306, 304)),
    312 -> Seq(Set(312, 307, 302, 301)),
    313 -> Seq(Set(313, 234), Set(313, 312, 310, 306)),
    314 -> Seq(Set(314, 299), Set(314, 311, 305, 300)),
    315 -> Seq(Set(315, 314, 306, 305)),
    316 -> Seq(Set(316, 181), Set(316, 309, 305, 304)),
    317 -> Seq(Set(317, 315, 313, 310)),
    318 -> Seq(Set(318, 313, 312, 310)),
    319 -> Seq(Set(319, 283), Set(319, 318, 317, 308)),
    320 -> Seq(Set(320, 319, 317, 316)),
    321 -> Seq(Set(321, 290), Set(321, 319, 316, 314)),
    322 -> Seq(Set(322, 255), Set(322, 321, 320, 305)),
    323 -> Seq(Set(323, 322, 320, 313)),
    324 -> Seq(Set(324, 321, 320, 318)),
    325 -> Seq(Set(325, 323, 320, 315)),
    326 -> Seq(Set(326, 325, 323, 316)),
    327 -> Seq(Set(327, 293), Set(327, 325, 322, 319)),
    328 -> Seq(Set(328, 323, 321, 319)),
    329 -> Seq(Set(329, 279), Set(329, 326, 323, 321)),
    330 -> Seq(Set(330, 328, 323, 322)),
    331 -> Seq(Set(331, 329, 325, 321)),
    332 -> Seq(Set(332, 209), Set(332, 325, 321, 320)),
    333 -> Seq(Set(333, 331), Set(333, 331, 329, 325)),
    334 -> Seq(Set(334, 333, 330, 327)),
    335 -> Seq(Set(335, 333, 328, 325)),
    336 -> Seq(Set(336, 335, 332, 329)),
    337 -> Seq(Set(337, 282), Set(337, 336, 331, 327)),
    338 -> Seq(Set(338, 336, 335, 332)),
    339 -> Seq(Set(339, 332, 329, 323)),
    340 -> Seq(Set(340, 337, 336, 329)),
    341 -> Seq(Set(341, 336, 330, 327)),
    342 -> Seq(Set(342, 217), Set(342, 341, 340, 331)),
    343 -> Seq(Set(343, 268), Set(343, 338, 335, 333)),
    344 -> Seq(Set(344, 338, 334, 333)),
    345 -> Seq(Set(345, 323), Set(345, 343, 341, 337)),
    346 -> Seq(Set(346, 344, 339, 335)),
    347 -> Seq(Set(347, 344, 337, 336)),
    348 -> Seq(Set(348, 344, 341, 340)),
    349 -> Seq(Set(349, 347, 344, 343)),
    350 -> Seq(Set(350, 297), Set(350, 340, 337, 336)),
    351 -> Seq(Set(351, 317), Set(351, 348, 345, 343)),
    352 -> Seq(Set(352, 346, 341, 339)),
    353 -> Seq(Set(353, 284), Set(353, 349, 346, 344)),
    354 -> Seq(Set(354, 349, 341, 340)),
    355 -> Seq(Set(355, 354, 350, 349)),
    356 -> Seq(Set(356, 349, 347, 346)),
    357 -> Seq(Set(357, 355, 347, 346)),
    358 -> Seq(Set(358, 351, 350, 344)),
    359 -> Seq(Set(359, 291), Set(359, 358, 352, 350)),
    360 -> Seq(Set(360, 359, 335, 334)),
    361 -> Seq(Set(361, 360, 357, 354)),
    362 -> Seq(Set(362, 299), Set(362, 360, 351, 344)),
    363 -> Seq(Set(363, 362, 356, 355)),
    364 -> Seq(Set(364, 297), Set(364, 363, 359, 352)),
    365 -> Seq(Set(365, 360, 359, 356)),
    366 -> Seq(Set(366, 337), Set(366, 362, 359, 352)),
    367 -> Seq(Set(367, 346), Set(367, 365, 363, 358)),
    368 -> Seq(Set(368, 361, 359, 351)),
    369 -> Seq(Set(369, 278), Set(369, 367, 359, 358)),
    370 -> Seq(Set(370, 231), Set(370, 368, 367, 365)),
    371 -> Seq(Set(371, 369, 368, 363)),
    372 -> Seq(Set(372, 369, 365, 357)),
    373 -> Seq(Set(373, 371, 366, 365)),
    374 -> Seq(Set(374, 369, 368, 366)),
    375 -> Seq(Set(375, 359), Set(375, 374, 368, 367)),
    376 -> Seq(Set(376, 371, 369, 368)),
    377 -> Seq(Set(377, 336), Set(377, 376, 374, 369)),
    378 -> Seq(Set(378, 335), Set(378, 374, 365, 363)),
    379 -> Seq(Set(379, 375, 370, 369)),
    380 -> Seq(Set(380, 333), Set(380, 377, 374, 366)),
    381 -> Seq(Set(381, 380, 379, 376)),
    382 -> Seq(Set(382, 301), Set(382, 379, 375, 364)),
    383 -> Seq(Set(383, 293), Set(383, 382, 378, 374)),
    384 -> Seq(Set(384, 378, 369, 368)),
    385 -> Seq(Set(385, 379), Set(385, 383, 381, 379)),
    386 -> Seq(Set(386, 303), Set(386, 381, 380, 376)),
    387 -> Seq(Set(387, 385, 379, 378)),
    388 -> Seq(Set(388, 387, 385, 374)),
    389 -> Seq(Set(389, 384, 380, 379)),
    390 -> Seq(Set(390, 301), Set(390, 388, 380, 377)),
    391 -> Seq(Set(391, 363), Set(391, 390, 389, 385)),
    392 -> Seq(Set(392, 386, 382, 379)),
    393 -> Seq(Set(393, 386), Set(393, 392, 391, 386)),
    394 -> Seq(Set(394, 259), Set(394, 392, 387, 386))
  )

  /** Second portion of known taps (a combined map hits the 64KB JVM method limit) */
  private def tapsSecond = Map(
    395 -> Seq(Set(395, 390, 389, 384)),
    396 -> Seq(Set(396, 371), Set(396, 392, 390, 389)),
    397 -> Seq(Set(397, 392, 387, 385)),
    398 -> Seq(Set(398, 393, 392, 384)),
    399 -> Seq(Set(399, 313), Set(399, 397, 390, 388)),
    400 -> Seq(Set(400, 398, 397, 395)),
    401 -> Seq(Set(401, 249), Set(401, 399, 392, 389)),
    402 -> Seq(Set(402, 399, 398, 393)),
    403 -> Seq(Set(403, 398, 395, 394)),
    404 -> Seq(Set(404, 215), Set(404, 400, 398, 397)),
    405 -> Seq(Set(405, 398, 397, 388)),
    406 -> Seq(Set(406, 249), Set(406, 402, 397, 393)),
    407 -> Seq(Set(407, 336), Set(407, 402, 400, 398)),
    408 -> Seq(Set(408, 407, 403, 401)),
    409 -> Seq(Set(409, 322), Set(409, 406, 404, 402)),
    410 -> Seq(Set(410, 407, 406, 400)),
    411 -> Seq(Set(411, 408, 401, 399)),
    412 -> Seq(Set(412, 265), Set(412, 409, 404, 401)),
    413 -> Seq(Set(413, 407, 406, 403)),
    414 -> Seq(Set(414, 405, 401, 398)),
    415 -> Seq(Set(415, 313), Set(415, 413, 411, 406)),
    416 -> Seq(Set(416, 414, 411, 407)),
    417 -> Seq(Set(417, 310), Set(417, 416, 414, 407)),
    418 -> Seq(Set(418, 417, 415, 403)),
    419 -> Seq(Set(419, 415, 414, 404)),
    420 -> Seq(Set(420, 412, 410, 407)),
    421 -> Seq(Set(421, 419, 417, 416)),
    422 -> Seq(Set(422, 273), Set(422, 421, 416, 412)),
    423 -> Seq(Set(423, 398), Set(423, 420, 418, 414)),
    424 -> Seq(Set(424, 422, 417, 415)),
    425 -> Seq(Set(425, 413), Set(425, 422, 421, 418)),
    426 -> Seq(Set(426, 415, 414, 412)),
    427 -> Seq(Set(427, 422, 421, 416)),
    428 -> Seq(Set(428, 323), Set(428, 426, 425, 417)),
    429 -> Seq(Set(429, 422, 421, 419)),
    430 -> Seq(Set(430, 419, 417, 415)),
    431 -> Seq(Set(431, 311), Set(431, 430, 428, 426)),
    432 -> Seq(Set(432, 429, 428, 419)),
    433 -> Seq(Set(433, 400), Set(433, 430, 428, 422)),
    434 -> Seq(Set(434, 429, 423, 422)),
    435 -> Seq(Set(435, 430, 426, 423)),
    436 -> Seq(Set(436, 271), Set(436, 432, 431, 430)),
    437 -> Seq(Set(437, 436, 435, 431)),
    438 -> Seq(Set(438, 373), Set(438, 436, 432, 421)),
    439 -> Seq(Set(439, 390), Set(439, 437, 436, 431)),
    440 -> Seq(Set(440, 439, 437, 436)),
    441 -> Seq(Set(441, 410), Set(441, 440, 433, 430)),
    442 -> Seq(Set(442, 440, 437, 435)),
    443 -> Seq(Set(443, 442, 437, 433)),
    444 -> Seq(Set(444, 435, 432, 431)),
    445 -> Seq(Set(445, 441, 439, 438)),
    446 -> Seq(Set(446, 341), Set(446, 442, 439, 431)),
    447 -> Seq(Set(447, 374), Set(447, 446, 441, 438)),
    448 -> Seq(Set(448, 444, 442, 437)),
    449 -> Seq(Set(449, 315), Set(449, 446, 440, 438)),
    450 -> Seq(Set(450, 371), Set(450, 443, 438, 434)),
    451 -> Seq(Set(451, 450, 441, 435)),
    452 -> Seq(Set(452, 448, 447, 446)),
    453 -> Seq(Set(453, 449, 447, 438)),
    454 -> Seq(Set(454, 449, 445, 444)),
    455 -> Seq(Set(455, 417), Set(455, 453, 449, 444)),
    456 -> Seq(Set(456, 454, 445, 433)),
    457 -> Seq(Set(457, 441), Set(457, 454, 449, 446)),
    458 -> Seq(Set(458, 255), Set(458, 453, 448, 445)),
    459 -> Seq(Set(459, 457, 454, 447)),
    460 -> Seq(Set(460, 399), Set(460, 459, 455, 451)),
    461 -> Seq(Set(461, 460, 455, 454)),
    462 -> Seq(Set(462, 389), Set(462, 457, 451, 450)),
    463 -> Seq(Set(463, 370), Set(463, 456, 455, 452)),
    464 -> Seq(Set(464, 460, 455, 441)),
    465 -> Seq(Set(465, 406), Set(465, 463, 462, 457)),
    466 -> Seq(Set(466, 460, 455, 452)),
    467 -> Seq(Set(467, 466, 461, 456)),
    468 -> Seq(Set(468, 464, 459, 453)),
    469 -> Seq(Set(469, 467, 464, 460)),
    470 -> Seq(Set(470, 321), Set(470, 468, 462, 461)),
    471 -> Seq(Set(471, 470), Set(471, 469, 468, 465)),
    472 -> Seq(Set(472, 470, 469, 461)),
    473 -> Seq(Set(473, 470, 467, 465)),
    474 -> Seq(Set(474, 283), Set(474, 465, 463, 456)),
    475 -> Seq(Set(475, 471, 467, 466)),
    476 -> Seq(Set(476, 461), Set(476, 475, 468, 466)),
    477 -> Seq(Set(477, 470, 462, 461)),
    478 -> Seq(Set(478, 357), Set(478, 477, 474, 472)),
    479 -> Seq(Set(479, 375), Set(479, 475, 472, 470)),
    480 -> Seq(Set(480, 473, 467, 464)),
    481 -> Seq(Set(481, 343), Set(481, 480, 472, 471)),
    482 -> Seq(Set(482, 477, 476, 473)),
    483 -> Seq(Set(483, 479, 477, 474)),
    484 -> Seq(Set(484, 379), Set(484, 483, 482, 470)),
    485 -> Seq(Set(485, 479, 469, 468)),
    486 -> Seq(Set(486, 481, 478, 472)),
    487 -> Seq(Set(487, 393), Set(487, 485, 483, 478)),
    488 -> Seq(Set(488, 487, 485, 484)),
    489 -> Seq(Set(489, 406), Set(489, 484, 483, 480)),
    490 -> Seq(Set(490, 271), Set(490, 485, 483, 481)),
    491 -> Seq(Set(491, 488, 485, 480)),
    492 -> Seq(Set(492, 491, 485, 484)),
    493 -> Seq(Set(493, 490, 488, 483)),
    494 -> Seq(Set(494, 357), Set(494, 493, 489, 481)),
    495 -> Seq(Set(495, 419), Set(495, 494, 486, 480)),
    496 -> Seq(Set(496, 494, 491, 480)),
    497 -> Seq(Set(497, 419), Set(497, 493, 488, 486)),
    498 -> Seq(Set(498, 495, 489, 487)),
    499 -> Seq(Set(499, 494, 493, 488)),
    500 -> Seq(Set(500, 499, 494, 490)),
    501 -> Seq(Set(501, 499, 497, 496)),
    502 -> Seq(Set(502, 498, 497, 494)),
    503 -> Seq(Set(503, 500), Set(503, 502, 501, 500)),
    504 -> Seq(Set(504, 502, 490, 483)),
    505 -> Seq(Set(505, 349), Set(505, 500, 497, 493)),
    506 -> Seq(Set(506, 411), Set(506, 501, 494, 491)),
    507 -> Seq(Set(507, 504, 501, 494)),
    508 -> Seq(Set(508, 399), Set(508, 505, 500, 495)),
    509 -> Seq(Set(509, 506, 502, 501)),
    510 -> Seq(Set(510, 501, 500, 498)),
    511 -> Seq(Set(511, 501), Set(511, 509, 503, 501)),
    512 -> Seq(Set(512, 510, 507, 504)),
    513 -> Seq(Set(513, 428), Set(513, 505, 503, 500)),
    514 -> Seq(Set(514, 511, 509, 507)),
    515 -> Seq(Set(515, 511, 508, 501)),
    516 -> Seq(Set(516, 514, 511, 509)),
    517 -> Seq(Set(517, 515, 507, 505)),
    518 -> Seq(Set(518, 485), Set(518, 516, 515, 507)),
    519 -> Seq(Set(519, 440), Set(519, 517, 511, 507)),
    520 -> Seq(Set(520, 509, 507, 503)),
    521 -> Seq(Set(521, 489), Set(521, 519, 514, 512)),
    522 -> Seq(Set(522, 518, 509, 507)),
    523 -> Seq(Set(523, 521, 517, 510)),
    524 -> Seq(Set(524, 357), Set(524, 523, 519, 515)),
    525 -> Seq(Set(525, 524, 521, 519)),
    526 -> Seq(Set(526, 525, 521, 517)),
    527 -> Seq(Set(527, 480), Set(527, 526, 520, 518)),
    528 -> Seq(Set(528, 526, 522, 517)),
    529 -> Seq(Set(529, 487), Set(529, 528, 525, 522)),
    530 -> Seq(Set(530, 527, 523, 520)),
    531 -> Seq(Set(531, 529, 525, 519)),
    532 -> Seq(Set(532, 531), Set(532, 529, 528, 522)),
    533 -> Seq(Set(533, 531, 530, 529)),
    534 -> Seq(Set(534, 533, 529, 527)),
    535 -> Seq(Set(535, 533, 529, 527)),
    536 -> Seq(Set(536, 533, 531, 529)),
    537 -> Seq(Set(537, 443), Set(537, 536, 535, 527)),
    538 -> Seq(Set(538, 537, 536, 533)),
    539 -> Seq(Set(539, 535, 534, 529)),
    540 -> Seq(Set(540, 361), Set(540, 537, 534, 529)),
    541 -> Seq(Set(541, 537, 531, 528)),
    542 -> Seq(Set(542, 540, 539, 533)),
    543 -> Seq(Set(543, 527), Set(543, 538, 536, 532)),
    544 -> Seq(Set(544, 538, 535, 531)),
    545 -> Seq(Set(545, 423), Set(545, 539, 537, 532)),
    546 -> Seq(Set(546, 545, 544, 538)),
    547 -> Seq(Set(547, 543, 540, 534)),
    548 -> Seq(Set(548, 545, 543, 538)),
    549 -> Seq(Set(549, 546, 545, 533)),
    550 -> Seq(Set(550, 357), Set(550, 546, 533, 529)),
    551 -> Seq(Set(551, 416), Set(551, 550, 547, 542)),
    552 -> Seq(Set(552, 550, 547, 532)),
    553 -> Seq(Set(553, 514), Set(553, 550, 549, 542)),
    554 -> Seq(Set(554, 551, 546, 543)),
    555 -> Seq(Set(555, 551, 546, 545)),
    556 -> Seq(Set(556, 403), Set(556, 549, 546, 540)),
    557 -> Seq(Set(557, 552, 551, 550)),
    558 -> Seq(Set(558, 553, 549, 544)),
    559 -> Seq(Set(559, 525), Set(559, 557, 552, 550)),
    560 -> Seq(Set(560, 554, 551, 549)),
    561 -> Seq(Set(561, 490), Set(561, 558, 552, 550)),
    562 -> Seq(Set(562, 560, 558, 551)),
    563 -> Seq(Set(563, 561, 554, 549)),
    564 -> Seq(Set(564, 401), Set(564, 563, 561, 558)),
    565 -> Seq(Set(565, 564, 559, 554)),
    566 -> Seq(Set(566, 413), Set(566, 564, 561, 560)),
    567 -> Seq(Set(567, 424), Set(567, 563, 557, 556)),
    568 -> Seq(Set(568, 558, 557, 551)),
    569 -> Seq(Set(569, 492), Set(569, 568, 559, 557)),
    570 -> Seq(Set(570, 503), Set(570, 563, 558, 552)),
    571 -> Seq(Set(571, 569, 566, 561)),
    572 -> Seq(Set(572, 571, 564, 560)),
    573 -> Seq(Set(573, 569, 567, 563)),
    574 -> Seq(Set(574, 561), Set(574, 569, 565, 560)),
    575 -> Seq(Set(575, 429), Set(575, 572, 570, 569)),
    576 -> Seq(Set(576, 573, 572, 563)),
    577 -> Seq(Set(577, 552), Set(577, 575, 574, 569)),
    578 -> Seq(Set(578, 562, 556, 555)),
    579 -> Seq(Set(579, 572, 570, 567)),
    580 -> Seq(Set(580, 579, 576, 574)),
    581 -> Seq(Set(581, 575, 574, 568)),
    582 -> Seq(Set(582, 497), Set(582, 579, 576, 571)),
    583 -> Seq(Set(583, 453), Set(583, 581, 577, 575)),
    584 -> Seq(Set(584, 581, 571, 570)),
    585 -> Seq(Set(585, 464), Set(585, 583, 582, 577)),
    586 -> Seq(Set(586, 584, 581, 579)),
    587 -> Seq(Set(587, 586, 581, 576)),
    588 -> Seq(Set(588, 437), Set(588, 577, 572, 571)),
    589 -> Seq(Set(589, 586, 585, 579)),
    590 -> Seq(Set(590, 497), Set(590, 588, 587, 578)),
    591 -> Seq(Set(591, 587, 585, 582)),
    592 -> Seq(Set(592, 591, 573, 568)),
    593 -> Seq(Set(593, 507), Set(593, 588, 585, 584)),
    594 -> Seq(Set(594, 575), Set(594, 586, 584, 583)),
    595 -> Seq(Set(595, 594, 593, 586)),
    596 -> Seq(Set(596, 592, 591, 590)),
    597 -> Seq(Set(597, 588, 585, 583)),
    598 -> Seq(Set(598, 597, 592, 591)),
    599 -> Seq(Set(599, 569), Set(599, 593, 591, 590)),
    600 -> Seq(Set(600, 599, 590, 589)),
    601 -> Seq(Set(601, 400), Set(601, 600, 597, 589)),
    602 -> Seq(Set(602, 596, 594, 591)),
    603 -> Seq(Set(603, 600, 599, 597)),
    604 -> Seq(Set(604, 600, 598, 589)),
    605 -> Seq(Set(605, 600, 598, 595)),
    606 -> Seq(Set(606, 602, 599, 591)),
    607 -> Seq(Set(607, 502), Set(607, 600, 598, 595)),
    608 -> Seq(Set(608, 606, 602, 585)),
    609 -> Seq(Set(609, 578), Set(609, 601, 600, 597)),
    610 -> Seq(Set(610, 483), Set(610, 602, 600, 599)),
    611 -> Seq(Set(611, 609, 607, 601)),
    612 -> Seq(Set(612, 607, 602, 598)),
    613 -> Seq(Set(613, 609, 603, 594)),
    614 -> Seq(Set(614, 613, 612, 607)),
    615 -> Seq(Set(615, 404), Set(615, 614, 609, 608)),
    616 -> Seq(Set(616, 614, 602, 597)),
    617 -> Seq(Set(617, 417), Set(617, 612, 608, 607)),
    618 -> Seq(Set(618, 615, 604, 598)),
    619 -> Seq(Set(619, 614, 611, 610)),
    620 -> Seq(Set(620, 619, 618, 611)),
    621 -> Seq(Set(621, 616, 615, 609)),
    622 -> Seq(Set(622, 325), Set(622, 612, 610, 605)),
    623 -> Seq(Set(623, 555), Set(623, 614, 613, 612)),
    624 -> Seq(Set(624, 617, 615, 612)),
    625 -> Seq(Set(625, 492), Set(625, 620, 617, 613)),
    626 -> Seq(Set(626, 623, 621, 613)),
    627 -> Seq(Set(627, 622, 617, 613)),
    628 -> Seq(Set(628, 405), Set(628, 626, 617, 616)),
    629 -> Seq(Set(629, 627, 624, 623)),
    630 -> Seq(Set(630, 628, 626, 623)),
    631 -> Seq(Set(631, 324), Set(631, 625, 623, 617)),
    632 -> Seq(Set(632, 629, 619, 613)),
    633 -> Seq(Set(633, 532), Set(633, 632, 631, 626)),
    634 -> Seq(Set(634, 319), Set(634, 631, 629, 627)),
    635 -> Seq(Set(635, 631, 625, 621)),
    636 -> Seq(Set(636, 632, 628, 623)),
    637 -> Seq(Set(637, 636, 628, 623)),
    638 -> Seq(Set(638, 637, 633, 632)),
    639 -> Seq(Set(639, 623), Set(639, 636, 635, 629)),
    640 -> Seq(Set(640, 638, 637, 626)),
    641 -> Seq(Set(641, 630), Set(641, 640, 636, 622)),
    642 -> Seq(Set(642, 523), Set(642, 636, 633, 632)),
    643 -> Seq(Set(643, 641, 640, 632)),
    644 -> Seq(Set(644, 634, 633, 632)),
    645 -> Seq(Set(645, 641, 637, 634)),
    646 -> Seq(Set(646, 397), Set(646, 635, 634, 633)),
    647 -> Seq(Set(647, 642), Set(647, 646, 643, 642)),
    648 -> Seq(Set(648, 647, 626, 625)),
    649 -> Seq(Set(649, 612), Set(649, 648, 644, 638)),
    650 -> Seq(Set(650, 647), Set(650, 644, 635, 632)),
    651 -> Seq(Set(651, 646, 638, 637)),
    652 -> Seq(Set(652, 559), Set(652, 647, 643, 641)),
    653 -> Seq(Set(653, 646, 645, 643)),
    654 -> Seq(Set(654, 649, 643, 640)),
    655 -> Seq(Set(655, 567), Set(655, 653, 639, 638)),
    656 -> Seq(Set(656, 646, 638, 637)),
    657 -> Seq(Set(657, 619), Set(657, 656, 650, 649)),
    658 -> Seq(Set(658, 603), Set(658, 651, 648, 646)),
    659 -> Seq(Set(659, 657, 655, 644)),
    660 -> Seq(Set(660, 657, 656, 648)),
    661 -> Seq(Set(661, 657, 650, 649)),
    662 -> Seq(Set(662, 365), Set(662, 659, 656, 650)),
    663 -> Seq(Set(663, 406), Set(663, 655, 652, 649)),
    664 -> Seq(Set(664, 662, 660, 649)),
    665 -> Seq(Set(665, 632), Set(665, 661, 659, 654)),
    666 -> Seq(Set(666, 664, 659, 656)),
    667 -> Seq(Set(667, 664, 660, 649)),
    668 -> Seq(Set(668, 658, 656, 651)),
    669 -> Seq(Set(669, 667, 665, 664)),
    670 -> Seq(Set(670, 517), Set(670, 669, 665, 664)),
    671 -> Seq(Set(671, 656), Set(671, 669, 665, 662)),
    672 -> Seq(Set(672, 667, 666, 661)),
    673 -> Seq(Set(673, 645), Set(673, 666, 664, 663)),
    674 -> Seq(Set(674, 671, 665, 660)),
    675 -> Seq(Set(675, 674, 672, 669)),
    676 -> Seq(Set(676, 435), Set(676, 675, 671, 664)),
    677 -> Seq(Set(677, 674, 673, 669)),
    678 -> Seq(Set(678, 675, 673, 663)),
    679 -> Seq(Set(679, 613), Set(679, 676, 667, 661)),
    680 -> Seq(Set(680, 679, 650, 645)),
    681 -> Seq(Set(681, 678, 672, 670)),
    682 -> Seq(Set(682, 681, 679, 675)),
    683 -> Seq(Set(683, 682, 677, 672)),
    684 -> Seq(Set(684, 681, 671, 666)),
    685 -> Seq(Set(685, 684, 682, 681)),
    686 -> Seq(Set(686, 489), Set(686, 684, 674, 673)),
    687 -> Seq(Set(687, 674), Set(687, 682, 675, 673)),
    688 -> Seq(Set(688, 682, 674, 669)),
    689 -> Seq(Set(689, 675), Set(689, 686, 683, 681)),
    690 -> Seq(Set(690, 687, 683, 680)),
    691 -> Seq(Set(691, 689, 685, 678)),
    692 -> Seq(Set(692, 393), Set(692, 687, 686, 678)),
    693 -> Seq(Set(693, 691, 685, 678)),
    694 -> Seq(Set(694, 691, 681, 677)),
    695 -> Seq(Set(695, 483), Set(695, 694, 691, 686)),
    696 -> Seq(Set(696, 694, 686, 673)),
    697 -> Seq(Set(697, 430), Set(697, 689, 685, 681)),
    698 -> Seq(Set(698, 483), Set(698, 690, 689, 688)),
    699 -> Seq(Set(699, 698, 689, 684)),
    700 -> Seq(Set(700, 698, 695, 694)),
    701 -> Seq(Set(701, 699, 697, 685)),
    702 -> Seq(Set(702, 665), Set(702, 701, 699, 695)),
    703 -> Seq(Set(703, 702, 696, 691)),
    704 -> Seq(Set(704, 701, 699, 692)),
    705 -> Seq(Set(705, 686), Set(705, 704, 698, 697)),
    706 -> Seq(Set(706, 697, 695, 692)),
    707 -> Seq(Set(707, 702, 699, 692)),
    708 -> Seq(Set(708, 421), Set(708, 706, 704, 703)),
    709 -> Seq(Set(709, 708, 706, 705)),
    710 -> Seq(Set(710, 709, 696, 695)),
    711 -> Seq(Set(711, 619), Set(711, 704, 703, 700)),
    712 -> Seq(Set(712, 709, 708, 707)),
    713 -> Seq(Set(713, 672), Set(713, 706, 703, 696)),
    714 -> Seq(Set(714, 691), Set(714, 709, 707, 701)),
    715 -> Seq(Set(715, 714, 711, 708)),
    716 -> Seq(Set(716, 533), Set(716, 706, 705, 704)),
    717 -> Seq(Set(717, 716, 710, 701)),
    718 -> Seq(Set(718, 717, 716, 713)),
    719 -> Seq(Set(719, 569), Set(719, 711, 710, 707)),
    720 -> Seq(Set(720, 718, 712, 709)),
    721 -> Seq(Set(721, 712), Set(721, 720, 713, 712)),
    722 -> Seq(Set(722, 491), Set(722, 721, 718, 707)),
    723 -> Seq(Set(723, 717, 710, 707)),
    724 -> Seq(Set(724, 719, 716, 711)),
    725 -> Seq(Set(725, 720, 719, 716), Set(758)),
    726 -> Seq(Set(726, 721), Set(726, 725, 722, 721)),
    727 -> Seq(Set(727, 547), Set(727, 721, 719, 716)),
    728 -> Seq(Set(728, 726, 725, 724), Set(761)),
    729 -> Seq(Set(729, 671), Set(729, 726, 724, 718)),
    730 -> Seq(Set(730, 583), Set(730, 726, 715, 711)),
    731 -> Seq(Set(731, 729, 725, 723), Set(764)),
    732 -> Seq(Set(732, 729, 728, 725), Set(765)),
    733 -> Seq(Set(733, 731, 726, 725), Set(766)),
    734 -> Seq(Set(734, 724, 721, 720), Set(767)),
    735 -> Seq(Set(735, 691), Set(735, 733, 728, 727)),
    736 -> Seq(Set(736, 730, 728, 723), Set(769)),
    737 -> Seq(Set(737, 732), Set(737, 736, 733, 732)),
    738 -> Seq(Set(738, 391), Set(738, 730, 729, 727)),
    739 -> Seq(Set(739, 731, 723, 721), Set(772)),
    740 -> Seq(Set(740, 587), Set(740, 737, 728, 716)),
    741 -> Seq(Set(741, 738, 733, 732), Set(774)),
    742 -> Seq(Set(742, 741, 738, 730), Set(775)),
    743 -> Seq(Set(743, 653), Set(743, 742, 731, 730)),
    744 -> Seq(Set(744, 743, 733, 731), Set(777)),
    745 -> Seq(Set(745, 487), Set(745, 740, 738, 737)),
    746 -> Seq(Set(746, 395), Set(746, 738, 733, 728)),
    747 -> Seq(Set(747, 743, 741, 737), Set(780)),
    748 -> Seq(Set(748, 744, 743, 733), Set(781)),
    749 -> Seq(Set(749, 748, 743, 742), Set(782)),
    750 -> Seq(Set(750, 746, 741, 734), Set(783)),
    751 -> Seq(Set(751, 733), Set(751, 750, 748, 740)),
    752 -> Seq(Set(752, 749, 732, 731), Set(785)),
    753 -> Seq(Set(753, 595), Set(753, 748, 745, 740)),
    754 -> Seq(Set(754, 735), Set(754, 742, 740, 735)),
    755 -> Seq(Set(755, 754, 745, 743), Set(2048)),
    756 -> Seq(Set(756, 407), Set(756, 755, 747, 740)),
    757 -> Seq(Set(757, 756, 751, 750)),
    758 -> Seq(Set(758, 757, 746, 741)),
    759 -> Seq(Set(759, 661), Set(759, 757, 756, 750)),
    760 -> Seq(Set(760, 757, 747, 734)),
    761 -> Seq(Set(761, 758), Set(761, 760, 759, 758)),
    762 -> Seq(Set(762, 679), Set(762, 761, 755, 745)),
    763 -> Seq(Set(763, 754, 749, 747)),
    764 -> Seq(Set(764, 761, 759, 758)),
    765 -> Seq(Set(765, 760, 755, 754)),
    766 -> Seq(Set(766, 757, 747, 744)),
    767 -> Seq(Set(767, 599), Set(767, 763, 760, 759)),
    768 -> Seq(Set(768, 764, 751, 749)),
    769 -> Seq(Set(769, 649), Set(769, 763, 762, 760)),
    770 -> Seq(Set(770, 768, 765, 756)),
    771 -> Seq(Set(771, 765, 756, 754)),
    772 -> Seq(Set(772, 765), Set(772, 767, 766, 764)),
    773 -> Seq(Set(773, 767, 765, 763)),
    774 -> Seq(Set(774, 589), Set(774, 767, 760, 758)),
    775 -> Seq(Set(775, 408), Set(775, 771, 769, 768)),
    776 -> Seq(Set(776, 773, 764, 759)),
    777 -> Seq(Set(777, 748), Set(777, 776, 767, 761)),
    778 -> Seq(Set(778, 403), Set(778, 775, 762, 759)),
    779 -> Seq(Set(779, 776, 771, 769)),
    780 -> Seq(Set(780, 775, 772, 764)),
    781 -> Seq(Set(781, 779, 765, 764)),
    782 -> Seq(Set(782, 453), Set(782, 780, 779, 773)),
    783 -> Seq(Set(783, 715), Set(783, 782, 776, 773)),
    784 -> Seq(Set(784, 778, 775, 771)),
    785 -> Seq(Set(785, 693), Set(785, 780, 776, 775)),
    786 -> Seq(Set(786, 782, 780, 771)),
    1024 -> Seq(Set(1024, 1015, 1002, 1001)),
    2048 -> Seq(Set(2048, 2035, 2034, 2029)),
    4096 -> Seq(Set(4096, 4095, 4081, 4069))
  )

}
